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A deterministic model for the occurrence and dynamics of multiple mutations in hierarchically organized tissues.

Werner B, Dingli D, Traulsen A - J R Soc Interface (2013)

Bottom Line: Our results hold for the average dynamics in a hierarchical tissue characterized by an arbitrary combination of proliferation parameters.We show that hierarchically organized tissues strongly suppress cells carrying multiple mutations and derive closed solutions for the expected size and diversity of clonal populations founded by a single mutant within the hierarchy.We discuss the example of childhood acute lymphoblastic leukaemia in detail and find good agreement between our predicted results and recently observed clonal diversities in patients.

View Article: PubMed Central - PubMed

Affiliation: Evolutionary Theory Group, Max Planck Institute for Evolutionary Biology, Plön, Germany.

ABSTRACT
Cancers are rarely caused by single mutations, but often develop as a result of the combined effects of multiple mutations. For most cells, the number of possible cell divisions is limited because of various biological constraints, such as progressive telomere shortening, cell senescence cascades or a hierarchically organized tissue structure. Thus, the risk of accumulating cells carrying multiple mutations is low. Nonetheless, many diseases are based on the accumulation of such multiple mutations. We model a general, hierarchically organized tissue by a multi-compartment approach, allowing any number of mutations within a cell. We derive closed solutions for the deterministic clonal dynamics and the reproductive capacity of single clones. Our results hold for the average dynamics in a hierarchical tissue characterized by an arbitrary combination of proliferation parameters. We show that hierarchically organized tissues strongly suppress cells carrying multiple mutations and derive closed solutions for the expected size and diversity of clonal populations founded by a single mutant within the hierarchy. We discuss the example of childhood acute lymphoblastic leukaemia in detail and find good agreement between our predicted results and recently observed clonal diversities in patients. This result can contribute to the explanation of very diverse mutation profiles observed by whole genome sequencing of many different cancers.

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(a) Number of cells carrying no mutation in compartments 1–31 arising from compartment 1 containing 1000 cells. Lines show equation (2.3), with parameters n0 = 1000, ε = 0.85, γ = 1.26, u = 10−6 and r0 = 1/400. Cells are more likely to differentiate than to self-renew and thus progressively travel into more committed compartments. Initially, the cell count increases, but cells get washed out in the long run. The time scale is determined by the number of stem cell divisions. A stem cell is assumed to divide once a year, thus after 400 stem cell divisions a year has passed. (b) Count of cells carrying 0–3 mutations in compartment 31, given by equation (2.4). We used the same parameters as in (a). Cells carrying multiple mutations are exponentially suppressed. (Online version in colour.)
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RSIF20130349F3: (a) Number of cells carrying no mutation in compartments 1–31 arising from compartment 1 containing 1000 cells. Lines show equation (2.3), with parameters n0 = 1000, ε = 0.85, γ = 1.26, u = 10−6 and r0 = 1/400. Cells are more likely to differentiate than to self-renew and thus progressively travel into more committed compartments. Initially, the cell count increases, but cells get washed out in the long run. The time scale is determined by the number of stem cell divisions. A stem cell is assumed to divide once a year, thus after 400 stem cell divisions a year has passed. (b) Count of cells carrying 0–3 mutations in compartment 31, given by equation (2.4). We used the same parameters as in (a). Cells carrying multiple mutations are exponentially suppressed. (Online version in colour.)

Mentions: For α > 0.5, the solution becomes a clonal wave, travelling through the hierarchy in time. In this case, the probability of differentiation is larger than the probability of self-renewal and thus cells progressively travel downstream (figure 3). The cell population founded by a single non-stem cell expands within the hierarchy initially, but gets washed out and vanishes in the long run. This is believed to be true for healthy homeostasis. For example, for the haematopoietic system, the differentiation probability was estimated to be ɛ = 0.85 [6]. As by far the most cell proliferations occur at the progenitor and more committed differentiation stages, this provides a natural protection for the organism against the accumulation of multiple mutations, as the survival time of most (non-stem cell-like) mutations is finite.Figure 3.


A deterministic model for the occurrence and dynamics of multiple mutations in hierarchically organized tissues.

Werner B, Dingli D, Traulsen A - J R Soc Interface (2013)

(a) Number of cells carrying no mutation in compartments 1–31 arising from compartment 1 containing 1000 cells. Lines show equation (2.3), with parameters n0 = 1000, ε = 0.85, γ = 1.26, u = 10−6 and r0 = 1/400. Cells are more likely to differentiate than to self-renew and thus progressively travel into more committed compartments. Initially, the cell count increases, but cells get washed out in the long run. The time scale is determined by the number of stem cell divisions. A stem cell is assumed to divide once a year, thus after 400 stem cell divisions a year has passed. (b) Count of cells carrying 0–3 mutations in compartment 31, given by equation (2.4). We used the same parameters as in (a). Cells carrying multiple mutations are exponentially suppressed. (Online version in colour.)
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4043170&req=5

RSIF20130349F3: (a) Number of cells carrying no mutation in compartments 1–31 arising from compartment 1 containing 1000 cells. Lines show equation (2.3), with parameters n0 = 1000, ε = 0.85, γ = 1.26, u = 10−6 and r0 = 1/400. Cells are more likely to differentiate than to self-renew and thus progressively travel into more committed compartments. Initially, the cell count increases, but cells get washed out in the long run. The time scale is determined by the number of stem cell divisions. A stem cell is assumed to divide once a year, thus after 400 stem cell divisions a year has passed. (b) Count of cells carrying 0–3 mutations in compartment 31, given by equation (2.4). We used the same parameters as in (a). Cells carrying multiple mutations are exponentially suppressed. (Online version in colour.)
Mentions: For α > 0.5, the solution becomes a clonal wave, travelling through the hierarchy in time. In this case, the probability of differentiation is larger than the probability of self-renewal and thus cells progressively travel downstream (figure 3). The cell population founded by a single non-stem cell expands within the hierarchy initially, but gets washed out and vanishes in the long run. This is believed to be true for healthy homeostasis. For example, for the haematopoietic system, the differentiation probability was estimated to be ɛ = 0.85 [6]. As by far the most cell proliferations occur at the progenitor and more committed differentiation stages, this provides a natural protection for the organism against the accumulation of multiple mutations, as the survival time of most (non-stem cell-like) mutations is finite.Figure 3.

Bottom Line: Our results hold for the average dynamics in a hierarchical tissue characterized by an arbitrary combination of proliferation parameters.We show that hierarchically organized tissues strongly suppress cells carrying multiple mutations and derive closed solutions for the expected size and diversity of clonal populations founded by a single mutant within the hierarchy.We discuss the example of childhood acute lymphoblastic leukaemia in detail and find good agreement between our predicted results and recently observed clonal diversities in patients.

View Article: PubMed Central - PubMed

Affiliation: Evolutionary Theory Group, Max Planck Institute for Evolutionary Biology, Plön, Germany.

ABSTRACT
Cancers are rarely caused by single mutations, but often develop as a result of the combined effects of multiple mutations. For most cells, the number of possible cell divisions is limited because of various biological constraints, such as progressive telomere shortening, cell senescence cascades or a hierarchically organized tissue structure. Thus, the risk of accumulating cells carrying multiple mutations is low. Nonetheless, many diseases are based on the accumulation of such multiple mutations. We model a general, hierarchically organized tissue by a multi-compartment approach, allowing any number of mutations within a cell. We derive closed solutions for the deterministic clonal dynamics and the reproductive capacity of single clones. Our results hold for the average dynamics in a hierarchical tissue characterized by an arbitrary combination of proliferation parameters. We show that hierarchically organized tissues strongly suppress cells carrying multiple mutations and derive closed solutions for the expected size and diversity of clonal populations founded by a single mutant within the hierarchy. We discuss the example of childhood acute lymphoblastic leukaemia in detail and find good agreement between our predicted results and recently observed clonal diversities in patients. This result can contribute to the explanation of very diverse mutation profiles observed by whole genome sequencing of many different cancers.

Show MeSH
Related in: MedlinePlus